Simple Trig Problem

I'm in high level math, but this little easy problem I came across I can't get!
Here it is (don't laugh):

The below shows the route of Diane's trip from her house to her job. Diane travels 16 miles from A to B, 15 miles from B to C, and 4 miles from C to D. If she were able to travel from A to D directly, how much shorter, in miles, would the trip be?
The figure is something like this (Ignore the dots I couldn't get it to work outherwise):
...........................................4
.....................................C-------D
.....................................|
.....................................|
.....................................|15
.....................................|
.....................................|
.............A----------------B
........................16

A quick explanation should do. I'm just having a mental block and its frusterating. The answer is 10 by the way.

However, try to answer the following questions:
1. What is the VERTICAL distance from the level of A to to the level of D?
2. What is the HORIZONTAL distance from the level of A to the level of D?
3,. What must therefore the distince between A and D be?